Question

Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that none are women?

Answer 1

Answer:    $\bold{\dfrac{1}{99}}$

Step-by-step explanation:

There are 5 men and 7 women, which is a total of 12 people.  Finding the probability that none of the four people are women is the same as saying that all four people are men.

$\dfrac{5\ men}{12\ total\ people}\ and\ \dfrac{4\ men\ remaining}{11\ people\ remaining}\ and\ \dfrac{3\ men}{10\ people}\ and\ \dfrac{2\ men}{9\ people}\\\\\\=\dfrac{5\times 4\times 3\times 2}{12\times 11\times 10\times 9}\\\\=\dfrac{(4\times 3)\times (2\times 5)}{12\times 11\times 10\times 9}\\\\=\dfrac{1}{11\times 9}\\\\=\dfrac{1}{99}$